[1] "year" "Area" "Seas"
[4] "Bio_smry" "SpawnBio" "Recruit_0"
[7] "retainB_1" "retainN_1" "retainB_2"
[10] "retainN_2" "retainB_3" "retainN_3"
[13] "retainB_4" "retainN_4" "retainB_5"
[16] "retainN_5" "deadB_1" "deadN_1"
[19] "deadB_2" "deadN_2" "deadB_3"
[22] "deadN_3" "deadB_4" "deadN_4"
[25] "deadB_5" "deadN_5" "F_1"
[28] "F_2" "F_3" "F_4"
[31] "F_5" "SPRratio" "rec_dev"
[34] "raw_rec_dev" "model_run" "iteration"
[37] "scenario" "end_year" "years_until_terminal"Comparing Future Red Tide Scenarios
These outputs are generated from the results__rt_2_fixed_2021 file. I took the SEDAR Red Grouper stock assessment and used SSMSE to introduce future red tide events in the OM and EM. There were 8 total scenarios:
- No red tide X no red tide: the base stock assessment with red tide events in 2005 and 2014.
- No red tide X 2 red tide: red tide in 2018 and 2021 in the EM.
- 2 red tide X no red tide: red tide in 2018 and 2021 in the OM, but not in the EM.
- 2 red tide X 2 red tide: red tide in 2018 and 2021 in the OM and EM, EM estimated.
- 2 red tide X 2 red tide fixed: red tide in 2018 and 2021 in the OM and EM, EM fixed.
- No red tide X all years red tide: no red tide in OM, all years red tide in EM.
- 2 red tide X all years red tide: red tide in 2018 and 2021 in OM, all years red tide in EM.
- red tide every 3 years X all years red tide: red tide every 3 years in OM starting in 2018, all years red tide in EM.
Import the results and summary files from the cloud.
Raw Data
Reviewing time series plots
List of the things we can plot with the ts_plot_variable function:
Here are the time series plots:
Figure 1. The fishing mortality of fleet 5 over time. This line plot demonstrates the frequency and magnitude of red tide events in the EM (black) and OM (orange) for each scenario. All 10 iterations of the OM and EM are plotted simultaneously so peaks are representative of the iteration with the highest value and not the overall trend. The OMs have fixed magnitudes and the EMs estimate a F_5 that varies in magnitude but has a median close to the fixed value in the OM.
Table 1. A summary of the Operating Model fleet 5 fishing mortality. These statistics only include values where F_5 > 0 and years > 2017.
| Scenario | Mean | Standard Dev | Median |
|---|---|---|---|
| rt_2_x_no_rt | 0.1 | 0 | 0.1 |
| rt_2_x_rt_2 | 0.1 | 0 | 0.1 |
| rt_2_x_rt_2_fixed | 0.1 | 0 | 0.1 |
| rt_2_x_all_yrs | 0.1 | 0 | 0.1 |
| rep_3_x_all_yrs | 0.1 | 0 | 0.1 |
Table 2. A summary of the Estimated Model fleet 5 fishing mortality. These statistics only include values where F_5 > 0 and years > 2017.
| Scenario | Mean | Standard Dev | Median |
|---|---|---|---|
| no_rt_x_rt_2 | 0.001 | 0.006 | 0.000 |
| rt_2_x_rt_2 | 0.091 | 0.017 | 0.095 |
| rt_2_x_rt_2_fixed | 0.100 | 0.000 | 0.100 |
| no_rt_x_all_yrs | 0.001 | 0.003 | 0.000 |
| rt_2_x_all_yrs | 0.007 | 0.021 | 0.000 |
| rep_3_x_all_yrs | 0.030 | 0.035 | 0.015 |
Figure 2. The biomass of fish killed by red tide over time. This line plot demonstrates the biomass removed by red tide. While fishing mortality is fixed in the OM, the biomass removed can vary depending on the available biomass.
Figure 3. The spawning stock biomass (SSB) over time. These plots best demonstrate the effects of the red tide mortality on the spawning availability, with the increased frequency and magnitude of red tides resulting in lower SSB.
Figure 4. The total retained biomass of the fishery over time. This is the sum of all columns starting with “RetainB” so it does not include discards or red tide mortality. This plot demonstrates how impactful high mortality events can reduce catch.
Reviewing derived quantities
Additional time series plots but derived quantities. Below is a list of all the derived quantity variables:
[1] "Value.SSB" "Value.Recr" "Value.SPRratio"
[4] "Value.F" "Value.Bratio" "Value.ForeCatch"
[7] "Value.OFLCatch" "Value.ForeCatchret" "Value.lnSPB"
[10] "year" "model_run" "iteration"
[13] "scenario" "end_year" "years_until_terminal"
Figure 5. Recruitment over time by scenario. Recruitment is determined by the Beverton-Holt equation using steepness, R0, and SigmaR. Steepness is fixed at 0.99. R0 and SigmaR were estimated in SEDAR 61 and SEDAR 88.
Figure 6 (same as figure 3). The spawning stock biomass (SSB) over time. These plots best demonstrate the effects of the red tide mortality on the spawning availability, with the increased frequency and magnitude of red tides resulting in lower SSB.
Figure 7. The Spawning Potential Ratio (SPR) over time by scenario. This is the spawning output with fishing:the spawning output without fishing so it is a higher value when the reproductive potential is high. SPR tends to spike when there is a red tide event.
Figure 8. The BRatio over time by scenario. The BRatio is the current SSB over the unfished SSB so the value indicates the status of the SSB relative to a unfished scenario. This can be usefull if there is a reference point for BRatio like 0.2 as a cut-off for overfished. Higher frequencies and magnitudes of red tide cause a BRatio less than 0.2 more often.
Figure 9. The total fishing mortality over time by scenario. The default scenario indicates that fishing over time has low variability. When Red tide events are introduced, the variability increases drastically as F includes red tide mortality. Since red tide is a by-catch fleet, it is included in this value.
Summarized Time Series
Stat of variables over time plots
dq of variables over time plots
Ratio Time Series
WARNING: EM:OM ratios do not work will with zeros in some fishing mortalities. If the EM and OM are both zero, the ratio is forced to 1. However, when the OM or EM is zero the result is either zero or na which has resulted in misleading F_5 plots. I changed the OM value to 0.001 to eliminate the Inf but it results in large ratios that expand the y-axis scale.We recommend the F.Value from dq plots to discuss overall changes in F across all fleets.
Fishing mortalities
My new method for plotting EM:OM involves creating separate OM and EM data frames, joining them by year, scenario, and iteration, then dividing the EM value/ OM value for every variable. That way when plotted it is truly the EM for each model run, year and iteration divided by the OM from the same year and iteration but one model run. If the om and em value are zero I changed the ratio to 1 because that means that the EM = OM.
Figure 10. Each fleet’s fishing mortality ratio (EM:OM) over time by scenario. The line indicates the median and the ribbon is the 25-75% quartiles. F_5 is consistently underestimated, it is more underestimated in future years where there is less data.
F_5
A zoomed in look at just F_5 from the previous plots.
Figure 11. Red tide mortality ratio (EM:OM) over time by scenario. The line indicates the median and the ribbon is the 25-75% quartiles. Red tide mortality is consistently underestimated, it is more underestimated in future years where there is less data.
F.Value from dqs
Biomass
Figure 12. Biomass ratio (EM:OM) over time by scenario. The line indicates the median and the ribbon is the 25-75% quartiles. Red tide mortality is consistently underestimated, it is more underestimated in future years where there is less data.
Recruitment
Figure 13. Recruitment ratio (EM:OM) over time by scenario. The line indicates the median and the ribbon is the 25-75% quartiles. Recruitment is not over or underestimated, but there are a few outliers where the EM overestimated by 10x.
SSB
Figure 14. SSB ratio (EM:OM) over time by scenario. The line indicates the median and the ribbon is the 25-75% quartiles. SSB is not over or underestimated, but it is more likely to be overestimated, the later years are overestimated. SSB may spike in response to red tide events based on the red_tide_regular_5_mortality_5 scenario.
Terminal Year
Plotting the same ratios as above but by the “time from the terminal year” instead of year. These plots use mean instead of median because there were too many “years until terminal” with no red tide which skewed to 1 and resulted in straight lines. F_5 in all of these plots was a straight line when median was used.
Fishing Mortality
Figure 15. Each fleet’s fishing mortality ratio (EM:OM) over the years from terminal year by scenario. The line indicates the mean and the ribbon is the 25-75% quartiles. F_5 is consistently underestimated, there is higher variation where there is less data.
F_5
A zoomed in look at just F_5 from the previous plots.
Figure 16. Red tide mortality ratio (EM:OM) over the years from terminal year by scenario. The line indicates the mean and the ribbon is the 25-75% quartiles. F_5 is consistently underestimated, there is higher variation where there is less data.
Biomass
Figure 17. Biomass ratio (EM:OM) over the years from terminal year by scenario. The line indicates the mean and the ribbon is the 25-75% quartiles. Red tide mortality is consistently underestimated, it is more underestimated in years where there is less data.
Recruitment
Figure 18. Recruitment ratio (EM:OM) over time by scenario. The line indicates the mean and the ribbon is the 25-75% quartiles. Recruitment is overestimated in the terminal year of the model run.
SSB
Figure 19. SSB ratio (EM:OM) over the years from the terminal year by scenario. The line indicates the mean and the ribbon is the 25-75% quartiles. SSB is underestimated when red tide is introduced, with higher variability in the terminal year of the default model.
Management Terms
Line Plots
Figure 20. Term plots are meant to be a “short term” (2000-2030) and “long term” (1989-2067) look at a few key parameters from the time series dataset. These plots demonstrate that red tide events correspond with SPR Ratio spikes, and can slowly decrease retained biomass or spawning biomass in the short term. In the long term, there are no trends.
Point Plots
Figure 21. Management Term plots are meant to be a “short term” (2000-2027) and “long term” (1989-2067) look at a few key parameters from the time series dataset. These plots demonstrate that red tide events correspond with SPR Ratio spikes, and can slowly decrease retained biomass or spawning biomass in the short term. In the long term, there are no trends. I tried to add median trend lines for the OM and EM but they aren’t very clear because of how the lines are colored.
Residual Error Plots
Residuals = EM - OM
This calculation does not have issues with zeros and estimates the error introduced to each variable by the different scenarios.
Long Term Residual Sums (1980-2050)
| Scenario | Commercial Catch Residual Sum | Recreational Catch Residual Sum | Red Tide Discards Residual Sum |
|---|---|---|---|
| no_rt | -33 | -172 | -507 |
| no_rt_x_rt_2 | -53 | -221 | -511 |
| rt_2_x_no_rt | -64 | -214 | -2131 |
| rt_2_x_rt_2 | -38 | -127 | -609 |
| rt_2_x_rt_2_fixed | -13 | -170 | -550 |
| no_rt_x_all_yrs | -8 | -172 | -182 |
| rt_2_x_all_yrs | -39 | -195 | -294 |
| rep_3_x_all_yrs | -11 | -25 | -1747 |
Short Term Residual Sums (2017-2022)
| Scenario | Commercial Catch Residual Sum | Recreational Catch Residual Sum | Red Tide Discards Residual Sum |
|---|---|---|---|
| no_rt | -9 | -32 | 0 |
| no_rt_x_rt_2 | -12 | -40 | 37 |
| rt_2_x_no_rt | 145 | 423 | -2517 |
| rt_2_x_rt_2 | 3 | 6 | -243 |
| rt_2_x_rt_2_fixed | -9 | -33 | -12 |
| no_rt_x_all_yrs | -10 | -34 | 57 |
| rt_2_x_all_yrs | 6 | 12 | -269 |
| rep_3_x_all_yrs | 4 | -7 | -297 |
Short Term Residual Proportions (2017-2022)
| Scenario | Commercial Catch Residual Sum (MT) | Recreational Catch Residual Sum (MT) | Red Tide Discards Residual Sum (MT) | Total Removals Residual Sum (MT) | Proportion of Residuals to Total (%) |
|---|---|---|---|---|---|
| no_rt | -0.08 | -0.42 | NaN | -40.63 | -0.22 |
| no_rt_x_rt_2 | -0.11 | -0.52 | Inf | -14.18 | -0.08 |
| rt_2_x_no_rt | 1.42 | 5.71 | -100.00 | -1949.25 | -9.69 |
| rt_2_x_rt_2 | 0.03 | 0.08 | -9.66 | -233.88 | -1.18 |
| rt_2_x_rt_2_fixed | -0.09 | -0.45 | -0.47 | -54.08 | -0.27 |
| no_rt_x_all_yrs | -0.09 | -0.45 | Inf | 12.37 | 0.07 |
| rt_2_x_all_yrs | 0.06 | 0.17 | -10.70 | -250.56 | -1.26 |
| rep_3_x_all_yrs | 0.03 | -0.10 | -11.71 | -301.04 | -1.51 |
Long Term Residual Sums (1980-2026)
| Scenario | Commercial Catch Residual Sum | Recreational Catch Residual Sum | Red Tide Discards Residual Sum |
|---|---|---|---|
| no_rt | -27 | -406 | -8648 |
| no_rt_x_rt_2 | -29 | -403 | -4898 |
| rt_2_x_no_rt | -651 | 287 | -14151 |
| rt_2_x_rt_2 | -94 | 18 | 1135 |
Short Term Residual Sums (2017-2022)
| Scenario | Commercial Catch Residual Sum | Recreational Catch Residual Sum | Red Tide Discards Residual Sum |
|---|---|---|---|
| no_rt | -14 | -57 | 0 |
| no_rt_x_rt_2 | -26 | -82 | 282 |
| rt_2_x_no_rt | 152 | 428 | -2517 |
| rt_2_x_rt_2 | 0 | 4 | 11 |
| rt_2_x_rt_2_fixed | -17 | -68 | -26 |
| no_rt_x_all_yrs | -16 | -52 | 156 |
| rt_2_x_all_yrs | 12 | 5 | -639 |
| rep_3_x_all_yrs | 7 | 2 | -322 |
Other Error Plots
Relative Error Plots
Inspired by Wetzel and Punt et al. 2011
I am going to attempt to make their Relative Error Plots.
RE = (E - T) / T
If the RE is NA (T = 0), the RE = 0. This introduces issues in the _all year scenarios where many of the T values are zero and the E > 0.
Cannot be produced because there are zeros in the OM and EM.
Cannot be calculated because of zeros in the EM and OM.
Figure 21. Relative error plots for each variable of interest zoomed in.
Figure 22. Relative error plots of each variable of interest on the same patchwork.
Figure 23. Relative error plots of each variable of interest with fixed x-limits between -1 and 1.
MAPE
Mean Average Percentage Error
WARNING: The equation for MAPE = abs(EM-OM)/OM so this can result in NA or Inf when the OM or EM is 0. This results in incorrect numbers for red tide mortality esspecially in the all_years treatments.
Notes: When there is no red tide in the OM, a matching EM results in less error in 2018 and a higher error in 2021. When there is a red tide in the OM, a matching EM results in less error in 2018 and more error in 2021.
Misspecifying the model does not increase the error, instead there is more error in 2021 and less error in 2018.
Notes: When there is no red tide in the OM, a matching EM results in less error in 2018 and a higher error in 2021. When there is a red tide in the OM, a matching EM results in less error in 2018 and more error in 2021.
Misspecifying the model does not increase the error, instead there is more error in 2021 and less error in 2018.
Relative Error
WARNING: The equation for RE = (EM-OM)/OM so this can result in NA or Inf when the OM or EM is 0. This results in incorrect numbers for red tide mortality especially in the all_years treatments.
Warning: Removed 1600 rows containing non-finite outside the scale range
(`stat_summary()`).
Removed 1600 rows containing non-finite outside the scale range
(`stat_summary()`).
Warning: Removed 4080 rows containing non-finite outside the scale range
(`stat_summary()`).
Removed 4080 rows containing non-finite outside the scale range
(`stat_summary()`).
Warning: Removed 3400 rows containing non-finite outside the scale range
(`stat_summary()`).
Removed 3400 rows containing non-finite outside the scale range
(`stat_summary()`).
Warning: Removed 8640 rows containing non-finite outside the scale range
(`stat_summary()`).
Removed 8640 rows containing non-finite outside the scale range
(`stat_summary()`).
Warning: Removed 6180 rows containing non-finite outside the scale range
(`stat_summary()`).
Removed 6180 rows containing non-finite outside the scale range
(`stat_summary()`).
Other Explorations
Exploring Recruitment
“rec_dev” “raw_rec_dev” “Recruit_0”
Ro Exploration
Extracted the R0 from SR_LN_R0 from the summary$scalar.
Ratios of Rec, SPR, and SSB
EM:OM ratios in the new format for variables that don’t have zeros.
Red Tide Year Comparisons
| year | scenario | EM_2047 | OM | Residual |
|---|---|---|---|---|
| 2005 | no_rt | 0.215 | 0.224 | -0.009 |
| 2005 | no_rt_x_rt_2 | 0.214 | 0.224 | -0.010 |
| 2005 | rt_2_x_no_rt | 0.223 | 0.224 | -0.001 |
| 2005 | rt_2_x_rt_2 | 0.217 | 0.224 | -0.006 |
| 2005 | rt_2_x_rt_2_fixed | 0.214 | 0.224 | -0.010 |
| 2005 | no_rt_x_all_yrs | 0.215 | 0.224 | -0.009 |
| 2005 | rt_2_x_all_yrs | 0.216 | 0.224 | -0.008 |
| 2005 | rep_3_x_all_yrs | 0.219 | 0.224 | -0.005 |
| 2014 | no_rt | 0.166 | 0.181 | -0.014 |
| 2014 | no_rt_x_rt_2 | 0.165 | 0.181 | -0.015 |
| 2014 | rt_2_x_no_rt | 0.207 | 0.181 | 0.027 |
| 2014 | rt_2_x_rt_2 | 0.171 | 0.181 | -0.010 |
| 2014 | rt_2_x_rt_2_fixed | 0.166 | 0.181 | -0.015 |
| 2014 | no_rt_x_all_yrs | 0.167 | 0.181 | -0.014 |
| 2014 | rt_2_x_all_yrs | 0.171 | 0.181 | -0.009 |
| 2014 | rep_3_x_all_yrs | 0.172 | 0.181 | -0.008 |
| 2018 | no_rt | 0.000 | 0.000 | 0.000 |
| 2018 | no_rt_x_rt_2 | 0.000 | 0.000 | 0.000 |
| 2018 | rt_2_x_no_rt | 0.000 | 0.100 | -0.100 |
| 2018 | rt_2_x_rt_2 | 0.095 | 0.100 | -0.005 |
| 2018 | rt_2_x_rt_2_fixed | 0.100 | 0.100 | 0.000 |
| 2018 | no_rt_x_all_yrs | 0.000 | 0.000 | 0.000 |
| 2018 | rt_2_x_all_yrs | 0.085 | 0.100 | -0.015 |
| 2018 | rep_3_x_all_yrs | 0.080 | 0.100 | -0.020 |
| 2021 | no_rt | 0.000 | 0.000 | 0.000 |
| 2021 | no_rt_x_rt_2 | 0.003 | 0.000 | 0.003 |
| 2021 | rt_2_x_no_rt | 0.000 | 0.100 | -0.100 |
| 2021 | rt_2_x_rt_2 | 0.087 | 0.100 | -0.013 |
| 2021 | rt_2_x_rt_2_fixed | 0.100 | 0.100 | 0.000 |
| 2021 | no_rt_x_all_yrs | 0.000 | 0.000 | 0.000 |
| 2021 | rt_2_x_all_yrs | 0.074 | 0.100 | -0.026 |
| 2021 | rep_3_x_all_yrs | 0.065 | 0.100 | -0.035 |
The OM mean is the solid line, the EM mean is the dashed line.
Absolute Error Plots
AE = abs(EM - OM)
This is a unidirectional error. So we ended up preferring Residual Sums. But I’ve kept these plots for reference. Mean Absolute Error (MAE) and Symmetric Mean Absolute Percentage Error (SMAPE) were removed because they had issues with zeros in the red tide fleet.
